Information on Result #1045300
Linear OOA(9114, 89, F9, 3, 74) (dual of [(89, 3), 153, 75]-NRT-code), using construction X applied to AG(3;F,156P) ⊂ AG(3;F,174P) based on
- linear OOA(996, 77, F9, 3, 74) (dual of [(77, 3), 135, 75]-NRT-code), using algebraic-geometric NRT-code AG(3;F,156P) [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- linear OOA(978, 77, F9, 3, 56) (dual of [(77, 3), 153, 57]-NRT-code), using algebraic-geometric NRT-code AG(3;F,174P) [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78 (see above)
- linear OOA(918, 12, F9, 3, 17) (dual of [(12, 3), 18, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(918, 16, F9, 3, 17) (dual of [(16, 3), 30, 18]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,30P) [i] based on function field F/F9 with g(F) = 1 and N(F) ≥ 16, using
- discarding factors / shortening the dual code based on linear OOA(918, 16, F9, 3, 17) (dual of [(16, 3), 30, 18]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3228, 178, F3, 3, 74) (dual of [(178, 3), 306, 75]-NRT-code) | [i] | Trace Code for OOAs | |